Abstract:

Vertex-distinguishing-equitable total coloring (VDETC) of some mycielski graphs was studied, and obtained the vertex-distinguishing-equitable total chromatic numbers of mycielski graphs of path, cycle, star and fan by using constructive method, which satisfy the conjecture on VDETC.

Key words: mycielski graph; vertex-distinguishing-equitable total coloring; vertex-distinguishing-equitable total chromatic number